Problem: $\dfrac{2}{9} \div \dfrac{9}{8} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{9}{8}$ is $\dfrac{8}{9}$ Therefore: $ \dfrac{2}{9} \div \dfrac{9}{8} = \dfrac{2}{9} \times \dfrac{8}{9} $ $ \phantom{\dfrac{2}{9} \times \dfrac{8}{9}} = \dfrac{2 \times 8}{9 \times 9} $ $ \phantom{\dfrac{2}{9} \times \dfrac{8}{9}} = \dfrac{16}{81} $